Question: Simplify to lowest terms. $\dfrac{20}{28}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 20 and 28? $20 = 2\cdot2\cdot5$ $28 = 2\cdot2\cdot7$ $\mbox{GCD}(20, 28) = 2\cdot2 = 4$ $\dfrac{20}{28} = \dfrac{5 \cdot 4}{ 7\cdot 4}$ $\hphantom{\dfrac{20}{28}} = \dfrac{5}{7} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{20}{28}} = \dfrac{5}{7} \cdot 1$ $\hphantom{\dfrac{20}{28}} = \dfrac{5}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{20}{28}= \dfrac{2\cdot10}{2\cdot14}= \dfrac{2\cdot 2\cdot5}{2\cdot 2\cdot7}= \dfrac{5}{7}$